Viral dynamic modelling of nirmatrelvir against in vitro SARS-COV-2 infection with different treatment initiation times

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Viral dynamic modelling of nirmatrelvir against in vitro SARS-COV-2 infection with different treatment initiation times

Xualin Liu¹, Kaley Hanrahan², Sean Avedissian³, Evelyn Franco^2,4, Coen van Hasselt¹, Ashley Brown^2,4 and Anne-Grete Märtson¹

¹Division of Systems Pharmacology and Pharmacy, Leiden Academic Centre for Drug Research, Leiden University; ²Institute for Therapeutic Innovation, Department of Medicine, College of Medicine, University of Florida; ³Department of Pharmacy Practice and Science, University of Nebraska Medical Center; ⁴Department of Pharmaceutics, College of Pharmacy, University of Florida

Background: The timing of antiviral treatment initiation plays an important role in drug efficacy. In vitro experiments have shown that delayed therapy initiation significantly decreased the antiviral efficacy of nirmatrelvir against SARS-CoV-2 infection. Further investigation is needed to gain understanding of the relationship between viral dynamics and the timing of treatment initiation to achieve better treatment response and to utilize existing SARS-CoV-2 data for emerging viral pathogens.

Aims: The aim of this study is to investigate the SARS-CoV-2 viral dynamics using a systems pharmacology modelling, which incorporates viral load profile and the effect of therapy delay.

Methods: In vitro data were obtained from antiviral experiments with five drug concentrations (0.004, 0.0156, 0.0625, 0.25 and 1 μg/mL) alongside a non-treatment control. The viral dynamic modelling was performed using the R package nlmixr2.

A target cell-limited (TCL) model and TCL model with eclipse phase (TCLE) in combination with different drug effect models were tested. Viral kinetic parameters such as viral infection rate (β), death rate of infected cells (δ) and viral production rate (ρ) were first estimated using control group data. A direct effect model was then incorporated to describe the antiviral effect when there was no treatment delay. An indirect response model was adapted to modify the drug effect when the treatment was delayed. An additive residual error model was applied in all the tested models. The estimation was performed using the first-order conditional estimation with interaction (FOCEi) method. Models were evaluated and selected based on objective function value (OFV) and goodness of fit (GOF).

Results: The in vitro data were well captured by a TCL model with sigmoid E_max drug effect. A direct effect model could best describe the concentration–effect relationship when the treatment started from day 0, while an adapted indirect response model had better performance when the therapy initiated from day 1 onwards, by adding a response controlling factor (k).

The final estimates (RSE%) of viral kinetic parameters (β = 1.52 × 10⁻⁷ (2.12%) 1/PFU/day, δ = 2.43 (62.1%) 1/day, ρ = 86.9 (4.92%) PFU/cell/day) and drug effect parameters (E_max = 1, Hill coefficient = 1.64 [57.7%], EC50 [no therapy delay] = 0.039 [8.36%] μg/mL, EC50 [with therapy delay] = 0.017 [7.64%] μg/mL, k = 2.48 [26.1%]) fit the experimental data well.

Conclusions: A TCL model with sigmoid E_max drug effect model was developed to characterize the concentration-effect relationship of nirmatrelvir against SARS-CoV-2. Following this, the model will be validated with clinical data. This systems pharmacology model is an excellent tool to estimate therapy success and failure in SARS-Cov-2 after. In the future, the model can be applied to other emerging viruses to test novel therapeutics.